Dear Ahmad,

you are right, the Nature is not real and imaginary in case of Electrochemical Impedance Spectroscopy, however the mathematical description might be. When you measure your electrical impedance, you compare the sinus voltage(for example) input with sinus current output and you divide the two in order to obtain the (complex) impedance (V/I) and/or (complex) admittance(I/V). In general, the measured output wave will be phase shifted relative to the input wave. Instead of working with cos(wt+delta) and cos(wt), you use complex numbers and mathematics become much more simple. If the phase shift delta is zero, your complex impedance "collapses" to real Ohmic resistance. please consult:

Lectures on Physics - Volume II (R.Feynman, Addison Wesley 1966), chapter. 22-1

Electrochemical Impedance Spectroascopy (M.E.Orazem,B.Tribollet, Wiley 2008)

So , remember, when the harmonic (sin,cos) input and the harmonic output are not in phase, you can use complex numbers to describe their relationship and do the calculations. In principle though , you do not have to do that.

With regards

Petr

Thank you for your answer dear Dr. Petr Viscor. i wish you add more explanation so that i can satisfy a professional physicist.

Dear Ahmad,

I am happy that my comment might have helped you a bit. Unfortunately, in order to add more, I would have to give a whole lecture on the use of the complex numbers in physics in general and for Impedance Spectroscopy in particular. And to that I have to add that it will never be as good as Richard Feynman approach. Therefore the two references that I found as the most relevant.

Regards

Petr

Thank you for your time and consideration dear Dr. Peter Viscor.